Amoure0723
Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

Leila puts an integer into the "In" box of each machine.
She finds that the answer that appears in the "Out" box of Machine A is the same as the
answer that appears in the "Out" box of Machine B.
What was the answer produced by both machines?
Show how you figured it out

Sagot :

MrRoyal

The machines represent equivalent expressions.

The output produced by both machines is 372

The equation represented on machine A is:

[tex]\mathbf{y = 2(5x + 3) - 24}[/tex]

The equation represented on machine B is:

[tex]\mathbf{y = 4(2(x + 11) - 7)}[/tex]

Where: x and y represent the inputs and the outputs, respectively

When the outputs are the same, it means:

[tex]\mathbf{y = y}[/tex]

So, we have:

[tex]\mathbf{2(5x + 3) - 24 = 4(2(x + 11) - 7)}[/tex]

Open brackets

[tex]\mathbf{10x + 6 - 24 = 8x + 88 - 28}[/tex]

[tex]\mathbf{10x - 18 = 8x + 60}[/tex]

Collect like terms

[tex]\mathbf{10x - 8x = 18 + 60}[/tex]

[tex]\mathbf{2x = 78 }[/tex]

Divide both sides by 2

[tex]\mathbf{x = 39 }[/tex]

Substitute 39 for x in [tex]\mathbf{y = 2(5x + 3) - 24}[/tex]

[tex]\mathbf{y = 2 \times (5 \times 39 + 3) - 24}[/tex]

[tex]\mathbf{y = 372}[/tex]

Hence, the output produced by both machines is 372

Read more about equivalent expressions at:

https://brainly.com/question/15715866

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.